I believe you are talking about soundwaves only, so I'll approach the answer from there.
The instant values a signal takes don't tell much about the sound it may generate. If a signal is zero at a certain instant $t_0$, it doesn't mean that at that moment there is silence. A single sample can't represent any sound because only oscillations can generate sound. I hope you see why a single sample can't possibly represent an oscillation of any kind.
Take for example a perfect sinewave. The signal $x(t)=\sin(t)$ is $0$ for infinite values of $t$, but the sound you hear is nonetheless uniform and constant. Also, it takes both positive and negative values, but the note you hear is always the same.
If a signal is $0$ for a given period of time though, then for that interval there will be silence indeed. In fact, if a signal is constant for a given period of time (not necessarily $0$), you will hear no sound at all (but you would be wasting power nonsensically).
In a nutshell, the instant values of a signal represent no sound whatsoever. It's the change over time of these values that can represent and generate sounds.
Truthfully, the zero isn't really zero at all, just a relative value.
When an audio signal is recorded, the signal values represent variations in air pressure around a central average value.
When an audio signal is played back, the zero represents the resting position of the speaker cone.
When a signal as no ampitude (all samples are zero) then there is no sound. An individual sample (as already pointed out) is meaningless in this context. However, a DC signal (all samples the same value) will not make a sound either. (With coupling capacitors, the speaker cone will return to resting position, but that is a different story).